It is hard to separate the word “perfect” from its moral connotations. Its synonyms pose similar problems. Perhaps the term “complete,” or “perfectly complete,” may be the best explanation for the sense of the question, “What would the perfect democracy look like?”
It is also hard to imagine the wholly new. When I picture a perfect democracy, I can only craft a collage of images I’ve seen before. A school of fish comes to mind. The school changes direction and form according to the aggregate and individual choices of the fish. Any fish may vote at any time. No fish sets agenda or limits voting options. Except by its physical presence. It is possible that those on the outer edge of the school may momentarily have more discretionary power than inside fish, by mere fact of having more open space available to move to. Though this disparity may be eventually averaged away, at any one moment, some fish may have votes that count more than the votes of others.
Other possible models, such as the genome or another type of swarm, have similar flaws. At some point, some member of the group ends up with more decision-making power than another. Even elementary particles suffer from hierarchy. An atom’s outer-most layer of electrons have far greater consequence than electrons with lower energy levels. Perhaps we must wait for the heat-death of the universe to find equality. In that case, perfect democracy is meaningless.
To imagine a non-trivial perfect democracy, I will dispense with the requirement that all members must be equally powerful at all times. Instead, the least powerful must be able to quickly become (split infinitive!) the most powerful. In this, a school of fish will suffice.